The second law: statement and applications

The second law of thermodynamics is often expressed as the fact that the entropy of an isolated system increases when a spontaneous change takes place. While this statement is true, a more general formulation can easily be presented to students. Starting from the Kelvin formulation of the second law, one can show that the entropy of a closed adiabatic system increases when an irreversible (spontaneous) process occurs. As a consequence, equilibrium is reached when the entropy of such a system has reached its maximum possible value given the constraints applied to the system. Information on the evolution of systems on which work can be done can be obtained even when temperature and pressure are ill-defined in the system during the process. An isolated system represents only a special case of a closed adiabatic system where no work is done on the system. We use this formulation of the second law to derive the significance of the Gibbs energy and show how it can be used to find the state of equilibrium of monobaric monothermal systems. We then provide one application of this formulation to show that the equilibrium state of a closed adiabatic system corresponds to maximum entropy. Additional examples and applications are provided in the supplemental material.